Method and apparatus to commission voltage sensors and branch circuit current sensors for branch circuit monitoring systems

ABSTRACT

A method and apparatus for detecting the wiring configuration of an electric power system based upon a particular voltage ratio that is determined for the electric power system. Also a method and apparatus for diagnosing voltage swap conditions in an electric power system. Finally, a method and apparatus for identifying virtual meters in an electric power system.

BACKGROUND

Field

The disclosed concept relates generally to electric power or energymeters in polyphase electric power systems, and more particularly to thecommissioning and diagnosis of voltage sensors and current sensors underdifferent wiring configurations for branch circuit monitoring systemsused in polyphase electric power systems.

Background Information

In a branch circuit monitoring system, a service panel typically has busbars that have polyphase voltages that can be measured using voltagesensors. In addition, the panel also has multiple main current sensorson the bus bars. Furthermore, the service panel can have branches andassociated branch circuit current sensors. For proper metering, it iscritical that those voltage and current sensors be configured correctly.Incorrect configurations often involve voltage sensors wired to wrongphases, branch circuit current sensors associated with wrong phases, orbranch circuit current sensors incorrectly grouped.

A conventional approach for commissioning and diagnosing a branchcircuit monitoring system is based on an understanding of the physicallayout of the system and the values measured by the voltage and currentsensors, which values are used to calculate real, reactive, and apparentpower values. Branch circuit current sensors are grouped based on thephysical layout, which are used to calculate branch power. A failure inthe understanding of the physical layout of the system often results inan incorrect configuration. Incorrect configurations may produce similarreal, reactive, apparent, and branch power values.

SUMMARY

In one embodiment, a method for determining a wiring configuration of anelectric power system is provided that includes determining a pluralityof Line to Line voltage measurement values for the electric powersystem, determining a voltage ratio for the electric power system usinga plurality of the Line to Line voltage measurement values, and usingthe voltage ratio to determine the wiring configuration of the electricpower system.

In another embodiment, a branch circuit meter module for an electricpower system is provided that includes a control system, wherein thecontrol system stores and is structured to execute a number of routines.The number of routines are structured to determine a plurality of Lineto Line voltage measurement values for the electric power system,determine a voltage ratio for the electric power system using aplurality of the Line to Line voltage measurement values, and use thevoltage ratio to determine a wiring configuration of the electric powersystem.

In still another embodiment, a method for diagnosing a neutral swapcondition in an electric power system employing a 3-phase 4-wire Wyewiring configuration or a 3-phase 4-wire Delta wiring configuration isprovided that includes determining a plurality of Line to Line voltagemeasurement values for the electric power system, determining a voltageratio for the electric power system using a plurality of the Line toLine voltage measurement values, and using the voltage ratio todetermine whether the neutral swap condition is present.

In still another embodiment, a branch circuit meter module for anelectric power system employing a 3-phase 4-wire Wye wiringconfiguration or a 3-phase 4-wire Delta wiring configuration is providedthat includes a control system, wherein the control system stores and isstructured to execute a number of routines. The number of routines arestructured to determine a plurality of Line to Line voltage measurementvalues for the electric power system, determine a voltage ratio for theelectric power system using a plurality of the Line to Line voltagemeasurement values, and use the voltage ratio to determine whether aneutral swap condition is present in the electric power system.

In yet another embodiment, a method for diagnosing a neutral swapcondition in an electric power system employing a single-phase 3-wireconfiguration is provided that includes determining a first Line toNeutral voltage measurement value for a first phase of the electricpower system using a first voltage sensor, determining a 30 second Lineto Neutral voltage measurement value for a second phase of the electricpower system using a second voltage sensor, and determining that aneutral swap condition exists with respect to the first voltage sensorif the first Line to Neutral voltage measurement value is lower than thesecond Line to Neutral voltage measurement value by at least one half,or determining that a neutral swap condition exists with respect to thesecond voltage sensor if the second Line to Neutral voltage measurementvalue is lower than the first Line to Neutral voltage measurement valueby at least one half.

In still another embodiment, a branch circuit meter module for anelectric power system employing a single-phase 3-wire wiringconfiguration is provided that includes a control system, wherein thecontrol system stores and is structured to execute a number of routines.The number of routines are structured to determine a first Line toNeutral voltage measurement value for a first phase of the electricpower system using a first voltage sensor, determine a second Line toNeutral voltage measurement value for a second phase of the electricpower system using a second voltage sensor, and determine that a neutralswap condition exists with respect to the first voltage sensor if thefirst Line to Neutral voltage measurement value is lower than the secondLine to Neutral voltage measurement value by at least one half, ordetermine that a neutral swap condition exists with respect to thesecond voltage sensor if the second Line to Neutral voltage measurementvalue is lower than the first Line to Neutral voltage measurement valueby at least one half.

In yet another embodiment, a method of diagnosing a phase swap conditionin an electric power system having a first phase, a second phase and athird phase and employing a 3-phase 4-wire Delta wiring configurationhaving a Hi-leg, wherein the Hi-leg is the first phase is provided. Themethod includes determining a first Line to Neutral voltage measurementvalue for the first phase, determining a second Line to Neutral voltagemeasurement value for the second phase, determining a third Line toNeutral voltage measurement value for the third phase, determiningwhether the first Line to Neutral voltage measurement value is a maximumof the first Line to Neutral voltage measurement value, the second Lineto Neutral voltage measurement value and the third Line to Neutralvoltage measurement value, and detecting that a phase swap condition ispresent if the first Line to Neutral voltage measurement value is notthe maximum.

In yet another embodiment, a branch circuit meter module for an electricpower system having a first phase, a second phase and a third phase andemploying a 3-phase 4-wire Delta wiring configuration having a Hi-leg,wherein the Hi-leg is the first phase is provided that includes acontrol system, wherein the control system stores and is structured toexecute a number of routines. The number of routines are structured todetermine a first Line to Neutral voltage measurement value for thefirst phase, determine a second Line to Neutral voltage measurementvalue for the second phase, determine a third Line to Neutral voltagemeasurement value for the third phase, determine whether the first Lineto Neutral voltage measurement value is a maximum of the first Line toNeutral voltage measurement value, the second Line to Neutral voltagemeasurement value and the third Line to Neutral voltage measurementvalue, and detect that a phase swap condition is present if the firstLine to Neutral voltage measurement value is not the maximum.

In still another embodiment, a method of identifying virtual meters inan electric power system employing a 3-phase 4-wire wye, a 3-phase3-wire delta, or a 1-phase 3-wire wiring configuration and having aplurality of branch circuits and a plurality of branch circuit currentsensors is provided, wherein each of the branch circuit current sensorsis associated with a respective one of the branch circuits, and whereinthe branch circuits and the branch circuit current sensors are arrangedin a physical layout wherein the branch circuits and the associatedbranch circuit current sensors are positioned in series adjacent to oneanother. The method includes determining a phase association for each ofthe branch circuit current sensors, testing the physical layout usingeach phase association to determine whether the branch circuit currentsensors are arranged in repeating phase order or reverse repeating phaseorder, responsive to determining that the branch circuit current sensorsare arranged in repeating phase order or reverse repeating phase order,for each branch circuit and the associated branch circuit currentsensor: (i) identifying a plurality of possible virtual meters includingthe associated branch circuit current sensor; (ii) for each possiblevirtual meter, calculating an associated measure of branch circuit phaseangle variance and an associated measure branch circuit currentvariance; and (iii) determining a candidate virtual meter for the branchcircuit based on the associated measures of branch circuit phase anglevariance and the associated measures of branch circuit currentvariances; and determining a number of identified virtual meters eachincluding two or more of the branch circuit current sensors based on thecandidate virtual meters. Also, branch circuit meter module is providedthat includes a control system, wherein the control system stores and isstructured to execute a number of routines structured to implement themethod just described.

BRIEF DESCRIPTION OF THE DRAWINGS

A full understanding of the disclosed concept can be gained from thefollowing description of the preferred embodiments when read inconjunction with the accompanying drawings in which:

FIGS. 1A and 1B are a schematic diagram of a branch circuit monitoringsystem according to one non-limiting exemplary embodiment in which thedisclosed concept may be implemented;

FIG. 2 is a circuit diagram of an exemplary 3-phase 4-wire Wye wiringconfiguration;

FIG. 3 is a circuit diagram of an exemplary 3-phase 3-wire Delta wiringconfiguration;

FIG. 4 is a circuit diagram of an exemplary 3-phase 4-wire Delta wiringconfiguration;

FIG. 5 is a circuit diagram of an exemplary 3-phase corner-groundedDelta wiring configuration;

FIG. 6 is a circuit diagram of an exemplary 2-phase Wye wiringconfiguration;

FIG. 7 is a circuit diagram of an exemplary single-phase 3-wire wiringconfiguration;

FIG. 8 is a schematic diagram of an overall architecture of a method andapparatus for current sensor diagnosis according to an exemplaryembodiment as implemented by/in the branch circuit monitoring system ofFIGS. 1A and 1B;

FIG. 9 is a phasor diagram of V_(AN), V_(BN), V_(CN) and V_(AB), V_(BC),V_(CA) in a 3-phase power system with balanced 3-phase voltages;

FIG. 10A is a phasor diagram showing the relationship between voltagesV_(An), V_(Bn), and current measurements I_(A), I_(B) according to oneembodiment of the disclosed concept;

FIG. 10B is a phasor diagram showing the relationship between voltagemeasurements V_(AN), V_(BN), V_(CN), and current measurements I_(A),I_(B) according to one embodiment of the disclosed concept;

FIG. 11 is a phasor diagram of voltages V_(An), V_(Bn), and voltagemeasurements V_(AN), V_(BN), V_(CN) according to one embodiment of thedisclosed concept;

FIG. 12. is a phasor diagram showing the relationship between voltagemeasurements V_(AN), V_(BN), and current measurements I_(A), I_(B)according to one embodiment of the disclosed concept; and

FIG. 13 is a phasor diagram showing the relationship between voltagemeasurements V_(AN) and current measurements I_(A) according to oneembodiment of the disclosed concept.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

As employed herein, the statement that two or more parts are “coupled”together shall mean that the parts are joined together either directlyor joined through one or more intermediate parts.

As employed herein, the term “number” shall mean one or an integergreater than one (i.e., a plurality).

As employed herein, the term “processor” means a programmable analogand/or digital device that can store, retrieve, and process data; acomputer; a workstation; a personal computer, a digital signalprocessor, a microprocessor; a microcontroller; a microcomputer; acentral processing unit; a controller, a mainframe computer, amini-computer, a server; a networked processor; or any suitableprocessing device or apparatus.

In one aspect, the disclosed concept provides a method and apparatusthat diagnoses current sensor polarities and phase associations indifferent wiring configurations for protective relays or electric poweror energy meters in polyphase electric power systems. The method andapparatus monitors phase angles between voltage and current waveforms,and diagnoses polarity and phase associations of current sensors indifferent wiring configurations using the monitored phase angles.Voltages and currents are measured via voltage and current sensors,respectively, and the measured voltages and currents are converted intorespective discrete-time voltage and current samples byanalog-to-digital converters. A phase angle is calculated between thevoltage and current for each phase, and the polarities and phaseassociations of the current sensors under different wiringconfigurations are diagnosed based on the phase angle. The diagnosisresults are output to indicate the determined polarities and phaseassociations. The diagnosis results may be stored and may be used fortroubleshooting or other diagnostic purposes

In another aspect, the disclosed concept provides a method and apparatusfor validating branch circuit current sensor diagnoses based on real andreactive power calculations. In still another aspect, the disclosedconcept provides a method and apparatus for detecting the wiringconfiguration of an electric power system based upon a particularvoltage ratio that is determined for the electric power system. In stilla further aspect, the disclosed concept provides a method and apparatusfor diagnosing voltage swap conditions in an electric power system. Instill a further aspect, the disclosed concept provides a method andapparatus for identifying virtual meters in an electric power system.The particulars of each of these aspects of the disclosed conceptaccording to various exemplary embodiments is described in detailherein.

FIGS. 1A and 1B are a schematic diagram of a branch circuit monitoringsystem 2 according to one non-limiting exemplary embodiment in which thedisclosed concept may be implemented. For ease of illustration, branchcircuit monitoring system 2 is broken up between the two separatefigures (FIGS. 1A and 1B), with FIG. 1A showing the wiring of the“Mains” and “Voltages” and FIG. 1B showing the branch circuit wiringconfiguration.

As seen in FIGS. 1A and 1B, branch circuit monitoring system 2 includesa main power source 4, such as, without limitation, a utility powersource, which in the illustrated embodiment is a three phase AC powersource. Main power source 4 provides phases A, B and C to a main breaker6 via a busbar 8 having conductors 8A, 8B, and 8C. Main breaker 6 is aconventional 3-pole circuit breaker for providing circuit protectionfunctionality to branch circuit monitoring system 2. The output of mainbreaker 6 is coupled to a busbar 10 having conductors 10A (which carriesphase A), 10B (which carries phase B), and 10C (which carries phase C).

As seen in FIGS. 1A and 1B, branch circuit monitoring system 2 furtherincludes a meter base 12 for providing power metering functionality forbranch circuit monitoring system 2. First and second branch circuitmeter modules 14A and 14B are coupled to meter base 12 as shown. Eachbranch circuit meter module 14 is structured to provide thefunctionality described briefly above and in greater detail herein.While in the illustrated embodiment branch circuit monitoring system 2includes first and second branch circuit meter modules 14A and 14B asjust described (each one associated with a particular group of branchcircuits), it will be understood that this is exemplary only, and thatthe functionality of the two branch circuit meter modules 14 may becombined into a single branch circuit meter module 14. Furthermore,branch circuit monitoring system 2 also include more than 2 branchcircuit meter modules 14, for example four, six or eight such modules.

In the exemplary embodiment, each branch circuit meter module 14A, 14Bcomprises a computing device having a control system including aprocessor 16A, 16B and a memory 18A, 18B. Processor 16A, 16B may be, forexample and without limitation, a microprocessor (μP), amicrocontroller, or some other suitable processing device, thatinterfaces with memory 18A, 18B. Memory 18A, 18B can be any one or moreof a variety of types of internal and/or external storage media such as,without limitation, RAM, ROM, EPROM(s), EEPROM(s), FLASH, and the likethat provide a storage register, i.e., a machine readable medium, fordata storage such as in the fashion of an internal storage area of acomputer, and can be volatile memory or nonvolatile memory. Memory 18A,18B has stored therein a number of routines that are executable byprocessor 16. One or more of the routines implement (by way ofcomputer/processor executable instructions) at least one embodiment ofthe methods discussed briefly above and in greater detail below forcommissioning and diagnosing voltage and current sensors forming a partof branch circuit monitoring system 2 under different wiringconfigurations.

As seen in FIGS. 1A and 1B, branch circuit monitoring system 2 alsoincludes a number of loads 20, labelled 20A-20F, which are powered bythe power received from main power source 4. In particular, as seen inFIG. 1B, each load 20 is coupled to one or more of the conductors 10A,10B, 10C of the main busbar 10 through an associated circuit breaker 22,which may be a 1-pole circuit breaker (labelled 22-1), a 2-pole circuitbreaker (labelled 22-2) or a 3-pole (labelled 22-3) circuit breaker, asappropriate.

Referring to FIG. 1A, branch circuit monitoring system 2 also includesvoltage sensors 24A, 24B, 24C for measuring the voltage of each phase onmain busbar 10, and current sensors 26A, 26B, 26C for measuring thecurrent of each phase on main busbar 10. Each voltage sensor 24 may be,for example and without limitation, a conventional potentialtransformer, and each current sensor 26 may be, for example and withoutlimitation, a conventional current transformer. Branch circuitmonitoring system 2 also includes a neutral voltage sensor 28 and aneutral current sensor 30 for measuring the voltage and current on aneutral line 32. The signals generated by the voltage sensors 24, thecurrent sensors 26, the neutral voltage sensor 28 and the neutralcurrent sensor 30 are provided to each branch circuit meter module 14for use as described herein.

Referring to FIG. 1B, branch circuit monitoring system 2 includes anumber of branch circuit current sensors 34, wherein, as seen in FIG.1B, each branch circuit current sensor 34 is associated with: (i) aparticular phase of main busbar 10, (ii) a particular pole of aparticular one of the circuit breakers 22, and (iii) a particular load20. Each branch circuit current sensor 34 may be, for example andwithout limitation, a conventional current transformer. The signalsgenerated by the current sensors 34 are provided to one of the branchcircuit meter modules 14 for use as described herein. In thenon-limiting exemplary embodiment, the signals generated by the branchcircuit current sensors 34 located on the left side of FIG. 1B andassociated with the circuit breakers 22 on the left side of main busbar10 are provided to branch circuit meter module 14A, and the signalsgenerated by the branch circuit current sensors 34 located on the rightside of FIG. 1B and associated with the circuit breakers 22 on the rightside of main busbar 10 are provided to branch circuit meter module 14B.

In branch circuit monitoring system 2 as just described, the voltage andcurrent sensors 24, 26, 28, 30 and 34 are operable to measure voltageand current waveforms, respectively. The voltage measurements aretypically acquired by the voltage sensors either from a phase withrespect to a separate phase, or from a phase with respect to a voltagereference point (e.g., neutral). In addition, there are two types ofcurrent sensors in branch circuit monitoring system 2. The first type ofcurrent sensor is the main current sensors 26, which are mounted on theconductors 10A, 10B, and 10C of main busbar 10 at an entry point to, forexample, a service panel, and measure aggregate currents for each phase.The second type of current sensor is the branch circuit current sensors34. Branch circuit current sensors 34 are mounted on each branch circuitassociated with a respective load 20, and measure the current of theindividual branch circuit.

In the exemplary embodiment, analog-to-digital converters 42, 44described elsewhere herein (FIG. 8) are used to convert voltage andcurrent measurements to discrete-time voltage and current samples,respectively, at a sampling frequency f_(S). The sampling frequencyf_(S) is typically expressed in hertz (Hz), or samples per cycle. Forexample, given an electric power system with a utility frequency off_(e)=60 Hz, a sampling frequency of 512 samples per cycle is equivalentto a sampling frequency of 30.720 Hz.

The voltage and current measurements described above are dependent onwiring configurations. For a branch circuit monitoring system 2 used ina 3-phase electric power system, the wiring configuration is typicallyone of the following possible cases: 3-Phase 4-Wire Wye; 3-Phase 3-WireDelta; 3-Phase 4-Wire Delta; 3-Phase Corner-Grounded Delta; 2-Phase Wye;Single-Phase 3-Wire; and Single-Phase 2-Wire. For each wiringconfiguration, the voltage and current sensors 24, 26, 28, 30 and 34 areconfigured accordingly to provide voltage and current measurements.

Description of Various Wiring Configurations

The description provided below describes the voltage and currentmeasurements that are associated with each particular wiringconfiguration listed above. That description will be helpful inunderstanding the particulars of the various aspects of the disclosedconcept described elsewhere herein.

3-Phase 4-Wire Wye

FIG. 2 is a circuit diagram 36A showing an exemplary 3-phase 4-wire Wyewiring configuration. In practice, the neutral N is connected to groundG through at least a resistor with high resistance to suppressover-voltages caused by re-striking arcs.

In the 3-phase 4-wire Wye wiring configuration, the voltage measurementsare typically acquired by voltage sensors either from a phase withrespect to a voltage reference point, or from a phase with respect to aseparate phase. For instance, when voltage measurements are acquired byvoltage sensors from a phase with respect to a voltage reference pointin FIG. 2, a voltage sensor intended for voltage measurement V_(AN) isconfigured to measure voltage from phase A to neutral N. A secondvoltage sensor intended for voltage measurement V_(BN) is configured tomeasure voltage from phase B to neutral N. A third voltage sensorintended for voltage measurement V_(CN) is configured to measure voltagefrom phase C to neutral N.

Alternatively, when voltage measurements are acquired by voltage sensorsfrom a phase with respect to a separate phase in FIG. 2, a voltagesensor intended for voltage measurement V_(AB) is configured to measurevoltage from phase A to phase B. A second voltage sensor intended forvoltage measurement V_(BC) is configured to measure voltage from phase Bto phase C. A third voltage sensor intended for voltage measurementV_(CA) is configured to measure voltage from phase C to phase A.

It is worth noting that voltage measurements V_(AB), V_(BC), V_(CA) arerelated to voltage measurements V_(AN), V_(BN), V_(CN) via:

V _(AB) =V _(AN) −V _(BN)  (1)

V _(BC) =V _(BN) −V _(BN)  (2)

V _(CA) =V _(CN) −V _(AN).  (3)

In FIG. 2, the positive direction of the phase A current measurementI_(A) is defined as from node “A” to node “n”, and the voltage V_(An) isdefined as the voltage at node “A” with respect to the voltage at node“n” in the same figure. Likewise, similar definitions apply to phases Band C quantities I_(B), I_(C), and V_(Bn), V_(Cn).

3-Phase 3-Wire Delta

FIG. 3 is a circuit diagram 36B showing an exemplary 3-phase 3-wireDelta wiring configuration. The voltage V_(AB) is defined as the voltageat node “A” with respect to the voltage at node “B,” and the currentI_(AB) is defined as the current flowing from node “A” to node “B.”Likewise, similar definitions apply to voltages V_(BC), V_(CA), andcurrents I_(BC), I_(CA).

In FIG., the positive direction of phase A current measurement I_(A) isdefined as from source to node “A”. Likewise, similar definitions applyto phases B and C quantities I_(B) and I_(C).

3-Phase 4-Wire Delta

FIG. 4 is a circuit diagram 36C showing an exemplary 3-phase 4-wireDelta wiring configuration. This is also known as high-leg Delta wiringconfiguration. In practice, the node “N” in a 3-phase 4-wire Deltasystem is usually accessible, while the node “n” in the same 3-phase4-wire Delta system is not always provided. Consequently, voltagemeasurements V_(AN), V_(BN), V_(CN), and current measurements I_(A),I_(B), I_(C) are available, while voltages V_(An), V_(Bn), V_(Cn) aretypically not available.

3-Phase Corner-Grounded Delta

FIG. 5 is a circuit diagram 36D showing 36C an exemplary 3-phasecorner-grounded Delta wiring configuration. In practice, the node “N” ina 3-phase corner-ground Delta system usually is accessible, while thenode “n” in the same 3-phase corner-ground Delta system is not alwaysprovided. Consequently, voltage measurements V_(AN), V_(CN), and currentmeasurements I_(A), I_(C) are available, while voltages V_(An), V_(Bn),V_(Cn) are typically not available.

2-Phase Wye

The 2-phase Wye wiring configuration is a special case of the 3-phase4-wire Wye wiring configuration. In a 2-phase Wye system, only 2 out of3 phases are used. For example, FIG. 6 is a circuit diagram 36E showingan exemplary 2-phase Wye wiring configuration with only Z_(A) and Z_(B)connected at load side. In practice, the neutral N is connected toground G through at least a resistor with high resistance to suppressover-voltages caused by re-striking arcs.

Single-Phase 3-Wire

FIG. 7 is a circuit diagram 36F showing an exemplary single-phase 3-wirewiring configuration. This is also known as split-phase wiringconfiguration. Unlike 3-phase wiring configurations, nodes “A”, “B” and“N” are all outputs from a center-tapped transformer, with neutral node“N” typically grounded.

According to FIG. 7, given balanced transformer outputs, voltagesmeasurements V_(AN) and V_(BN) have the following relationship:

V _(AN) =−V _(BN).  (4)

Single-Phase 2-Wire

The single-phase 2-wire wiring configuration is a special case of thesingle-phase 3-wire wiring configuration. In a single-phase 2-wiresystem, only 1 out of 2 phases are used. For example, referring to 7,when only Z_(A) is connected, then the original single-phase 3-wire Wyesystem becomes a single-phase 2-wire system.

Branch Circuit Current Sensor Diagnosis

One particular aspect of the disclosed concept provides a branch circuitcurrent sensor diagnosis methodology that determines whether a branchcircuit current sensor has been configured with a correct polarity andassociated with a correct phase. The branch circuit current sensordiagnosis of the disclosed concept, described in greater detail below,first obtains wiring configuration information, and then uses the phaseangle between voltage and current to determine the current sensor'sconfiguration.

In connection with implementing this aspect of the disclosed concept, anumber of methods for calculating phase angle between voltage andcurrent are provided. Also provided are diagnosis methods to determinewhether a branch circuit current sensor has been configured with acorrect polarity and associated with a correct phase which areparticular to each wiring configuration.

FIG. 8 shows an overall architecture of a method and apparatus ofcurrent sensor diagnosis according to an exemplary embodiment asimplemented by/in branch circuit monitoring system 2 including branchcircuit meter modules 14. The method and apparatus includes thefollowing five parts or stages: (1) voltage and current measurements 38and 40 are sensed by voltage sensors 24, 28 and current sensors 26, 30,34, respectively; (2) the voltage and current measurements 38 and 40 areconverted to respective voltage and current samples 46, 48 byanalog-to-digital converters (ADCs) 42, 44; (3) a phase angle 50 betweenthe voltage and current is typically calculated for phases A, B and C;(4) current sensor polarities and phase associations diagnoses 52 aredetermined based on predetermined wiring configurations 54 (seedescription provided elsewhere herein for a methodology forautomatically determining the wiring configurations 54 according to afurther aspect of the disclosed concept); and (5) diagnosis results 56are output, and may be stored and may be used for troubleshooting orother diagnostic purposes. A suitable processor 16 forming a part ofeach branch circuit meter modules 14 as described herein is employed forthe last three parts or stages 50, 52, 56. The processor 16 can becoupled to an example display 58 for the output of the diagnosis results56. Although two ADCs 42, 44 are shown, a single ADC can be employedhaving a plurality of channels for outputting digital samples of thesensed voltages and currents.

As just described, the branch circuit current sensor diagnosismethodology of the disclosed concept determines whether a branch circuitcurrent sensor 34 has been configured with a correct polarity andassociated with a correct phase. In particular, the methodology firstobtains wiring configuration information, and then uses the phase anglebetween voltage and current to determine the current sensor'sconfiguration. Described below are two alternative methods that may beused to calculate phase angle between voltage and current in order toimplement the branch circuit current sensor diagnosis methodology of thedisclosed concept.

In a first method, for each phase, such as phase A, B, or C shown inFIGS. 1A and 1B, the phase angle between voltage and current may becalculated by counting the numbers of samples N_(Z) from the voltagesample's zero-crossing time to the current sample's zero-crossing time.Because the sampling frequency f_(S) is a known quantity, the number ofsamples from the voltage sample's zero-crossing time to the currentsample's zero-crossing time may be converted to a time quantity T_(Z)(in seconds) via:

T _(Z) =N _(Z) /f _(S).  (5)

where f_(S) is in hertz (Hz).

Because the utility frequency f_(e) (in hertz) of the 3-phase electricpower system is typically a known quantity, the time quantity T_(Z) isfurther converted to a phase angle between voltage and current,typically expressed in degrees (°) via:

φ=rem(360·T _(Z) ·f _(e),360)  (6)

where rem(·, 360) denotes the remainder of a quantity after it isdivided by 360.

The operation wraps the phase angle between voltage and current to anon-negative value between 0 and 360°, and simplifies the subsequentcurrent sensor diagnosis.

Following the above definition, when the voltage and current waveformsare in phase with each other, then the voltage and current samples'zero-crossing times are identical. Consequently, the phase angle betweenvoltage and current is 0°. Otherwise, the phase angle between voltageand current is a positive value less than 360°.

In a second method, when real power P (in watts), apparent power S (involts·amperes), and leading/lagging information of each phase areavailable, the phase angle between voltage and current for each phase iscalculated by first calculating an intermediate phase angle φ′ usingTable 1 below.

TABLE 1 Method to Calculate Phase Angle P S Lead/Lag φ′= >0 ≠0 Lagging arccos(P/S) <0 ≠0 Lagging  arccos(P/S) <0 ≠0 Leading −arccos(P/S) >0 ≠0Leading −arccos(P/S) =0 ≠0 Lagging π/2 =0 ≠0 Leading −π/2  =0 =0Undefined Undefined

In Table 1, arccos(•) is an arccosine function whose range is between 0and π inclusive, i.e., 0≦arccos(•)≦π. For example, if P<0 and leading,then φ′=−arccos(P/S).

The phase angle between voltage and current is then obtained from theintermediate phase angle φ′ via:

φ=rem[(φ′+2π)·180/π,360].  (7)

Moreover, as described in detail below, according to a further aspect ofthe disclosed concept, each different wiring configuration describedherein has an associated set of rules for determining whether a branchcircuit current sensor in the wiring configuration has been configuredwith a correct polarity and associated with a correct phase that usesthe determined phase angle for the sensor in question.

More specifically, for a branch circuit current sensor 34 intended tomeasure phase A current in a 3-phase 4-wire Wye wiring configuration,there are 6 possible scenarios for this particular branch circuitcurrent sensor 34:

-   -   1) The branch circuit current sensor 34 is wired to phase A        current-carrying conductor with a normal polarity. Consequently,        the current measurement from the branch circuit current sensor        is I_(A).    -   2) The branch circuit current sensor 34 is wired to phase A        current-carrying conductor with a flipped polarity.        Consequently, the current measurement from the branch circuit        current sensor is −I_(A).    -   3) The branch circuit current sensor 34 is wired to phase B        current-carrying conductor with a normal polarity. Consequently,        the current measurement from the branch circuit current sensor        is I_(B).    -   4) The branch circuit current sensor 34 is wired to phase B        current-carrying conductor with a flipped polarity.        Consequently, the current measurement from the branch circuit        current sensor is −I_(B).    -   5) The branch circuit current sensor 34 is wired to phase C        current-carrying conductor with a normal polarity. Consequently,        the current measurement from the branch circuit current sensor        is I_(C).    -   6) The branch circuit current sensor 34 is wired to phase C        current-carrying conductor with a flipped polarity.        Consequently, the current measurement from the branch circuit        current sensor is −I_(C).

Similarly, a branch circuit current sensor 34 intended to measure phaseB or C current also has 6 possible scenarios in each case. According tothe disclosed concept, and as described in greater detail below, thebranch circuit current sensor diagnosis methodology determines whichscenario a particular branch circuit current sensor 34 has by analyzingthe phase angle between voltage and current according to a set of rules(in the form of a look-up table in the exemplary embodiment) that isspecific to the particular wiring configuration in question, wherein therules relate the phase angle to a particular sensor association andpolarity.

In connection with the disclosed concept, all voltage sensors 24, 28 areassumed to have been correctly configured in polarities and phaseassociations. For instance, in the 3-phase 4-wire Wye wiringconfiguration example above, a voltage sensor 24 intended for voltagemeasurement V_(AN) is configured correctly to measure voltage from phaseA to neutral N. A second voltage sensor 24 intended for voltagemeasurement V_(BN) is configured correctly to measure voltage from phaseB to neutral N. A third voltage sensor 24 intended for voltagemeasurement V_(CN) is configured correctly to measure voltage from phaseC to neutral N.

In addition, because most modern 3-phase electric power systems areregulated, 3-phase voltages are hence assumed to be balanced, i.e., thevoltage measurements V_(AN), V_(BN), V_(CN), when expressed in phasors,have the same amplitude, and are 120° degrees apart from each other.

Consequently, according to equations (1)-(3), voltage measurementsV_(AB), V_(BC), V_(CA), when expressed in phasors, all have the sameamplitude, and are 120° degrees apart from each other, as shown inphasor diagram 60 of FIG. 9.

For the purpose of the disclosed concept, a 3-phase symmetric load isassumed, i.e.:

Z _(A) =Z _(B) =Z _(C) =Z,  (8)

and the load impedance phase angle, φ, is limited to between 10° leading(capacitive load) and 50° lagging (inductive load). If the loadimpedance phase angle, φ, is expressed as a non-negative value between 0and 360°, then the above limit translates to 0°≦φ<50° and 350°≦φ<360°.

The above load impedance phase angle range includes: 1) purely resistiveloads, in which the load impedance phase angle is φ=0°; 2) a majorportion of inductive loads, including induction motors, in which theload impedance has a lagging phase angle, i.e., 0°≦φ<50°; and 3) certaincapacitive loads, in which the load impedance has a leading phase angle,i.e., 350°<φ<360°.

While the above assumption limits the load impedance phase angle φ to arange 0°≦φ<50° and 350°≦φ<360°, other load impedance phase angle rangescan be alternatively used. For example, in a system predominated byinductive loads, the load impedance phase angle φ may be alternativelyassumed to range from 20° lagging (inductive load) to 80° lagging(inductive load), i.e., 20°<φ<80°.

As noted above, for each wiring configuration described herein, thebranch circuit current sensor diagnosis has a different set of rules fordetermining sensor phase association and polarity based upon determinedphase angle. Thus, according to an aspect of the disclosed concept, eachparticular wiring configuration described herein has an associated table(referred to as a “Current Sensor Diagnosis Table”) that summarizes theset of rules applicable to particular wiring configuration. The currentsensor diagnosis methodology according to the disclosed conceptdetermines the current sensor's polarity and phase association byreading appropriate entries in the appropriate table. The Current SensorDiagnosis Tables that are applicable to the 3-Phase 4-Wire Wye, 3-Phase3-Wire Delta, 3-Phase 4-Wire Delta, and 3-Phase Corner-Grounded Deltawiring configurations are described in detail in the United StatesPatent Application Publication Number 2015/0042311, which is owned bythe assignee hereof and incorporated herein by reference in itsentirety. As a result, the rationale behind those tables is notdiscussed in detail herein. Instead, the Current Sensor Diagnosis Tablefor each of those wiring configurations is provided below (Tables 2-5)for convenience. Furthermore, one aspect of the disclosed concept is theprovision of Current Sensor Diagnosis Table for the 2-Phase Wye,Single-Phase 3-Wire, and Single-Phase 2-Wire wiring configurations, eachof which is described in detail below (Tables 6-8). Table 2. CurrentSensor Diagnosis for 3-Phase 4-Wire Wye Wiring Configuration

TABLE 2 Current Sensor Diagnosis for 3-Phase 4-Wire Wye WiringConfiguration φ_(A) φ_(B) φ_(C) 0° ≦ φ_(A) < 50° or I_(A) 0° ≦ φ_(B) <50° or I_(B) 0° ≦ φ_(C) < 50° or I_(C) 350° < φ_(A) < 360° 350° < φ_(B)< 360° 350° < φ_(C) < 360° 50° < φ_(A) < 110° −I_(C) 50° < φ_(B) < 110°−I_(A) 50° < φ_(C) < 110° −I_(B) 110° < φ_(A) < 170° I_(B) 110° < φ_(B)< 170° I_(C) 110° < φ_(C) < 170° I_(A) 170° < φ_(A) < 230° −I_(A) 170° <φ_(B) < 230° −I_(B) 170° < φ_(C) < 230° −I_(C) 230° < φ_(A) < 290° I_(C)230° < φ_(B) < 290° I_(A) 230° < φ_(C) < 290° I_(B) 290° < φ_(A) < 350°−I_(B) 290° < φ_(B) < 350° −I_(C) 290° < φ_(C) < 350° −I_(A)

TABLE 3 Current Sensor Diagnosis for 3-Phase 3-Wire Delta WiringConfiguration φ_(A) φ_(B) φ_(C) 0° ≦ φ_(A) < 50° or I_(A) 0° ≦ φ_(B) <50° or I_(B) 0° ≦ φ_(C) < 50° or I_(C) 350° < φ_(A) < 360° 350° < φ_(B)< 360° 350° < φ_(C) < 360° 50° < φ_(A) < 110° −I_(C) 50° < φ_(B) < 110°−I_(A) 50° < φ_(C) < 110° −I_(B) 110° < φ_(A) < 170° I_(B) 110° < φ_(B)< 170° I_(C) 110° < φ_(C) < 170° I_(A) 170° < φ_(A) < 230° −I_(A) 170° <φ_(B) < 230° −I_(B) 170° < φ_(C) < 230° −I_(C) 230° < φ_(A) < 290° I_(C)230° < φ_(B) < 290° I_(A) 230° < φ_(C) < 290° I_(B) 290° < φ_(A) < 350°−I_(B) 290° < φ_(B) < 350° −I_(C) 290° < φ_(C) < 350° −I_(A)

TABLE 4 Current Sensor Diagnosis for 3-Phase 4-Wire Delta WiringConfiguration φ_(A) φ_(B) φ_(C) 0° ≦ φ_(A) < 50° or I_(A) 20° < φ_(B) <80° I_(B) 320° < φ_(B) < 360° or I_(C) 350° < φ_(A) < 360° 0° ≦ φ_(B) <20° 50° < φ_(A) < 110° −I_(C) 80° < φ_(B) < 140° −I_(A) 20° < φ_(C) <80° −I_(B) 110° < φ_(A) < 170° I_(B) 140° < φ_(B) < 200° I_(C) 80° <φ_(C) < 140° I_(A) 170° < φ_(A) < 230° −I_(A) 200° < φ_(B) < 260° −I_(B)140° < φ_(C) < 200° −I_(C) 230° < φ_(A) < 290° I_(C) 260° < φ_(B) < 320°I_(A) 200° < φ_(C) < 260° I_(B) 290° < φ_(A) < 350° −I_(B) 320° < φ_(B)< 360° or −I_(C) 260° < φ_(C) < 320° −I_(A) 0° ≦ φ_(B) < 20°

TABLE 5 Current Sensor Diagnosis for 3-Phase Corner- Grounded DeltaWiring Configuration φ_(A) φ_(B) φ_(C) 20° < φ_(A) < 80° I_(A) N/A — 0°≦ φ_(A) < 20° or I_(C) 320° < φ_(A) < 360° 80° < φ_(A) < 140° −I_(C) N/A— 20° < φ_(C) < 80° −I_(B) 140° < φ_(A) < 200° I_(B) N/A — 80° < φ_(C) <140° I_(A) 200° < φ_(A) < 260° −I_(A) N/A — 140° < φ_(C) < 200° −I_(C)260° < φ_(A) < 320° I_(C) N/A — 200° < φ_(C) < 260° I_(B) 320°< φ_(A) <360° or −I_(B) N/A — 260° < φ_(C) < 320° −I_(A) 0° ≦ φ_(A) < 20°

The discussion will now switch to the Current Sensor Diagnosis table forthe 2-Phase Wye, Single-Phase 3-Wire, and Single-Phase 2-Wire wiringconfigurations.

With respect to 2-Phase Wye, the load impedance phase angle is limitedto between 10° leading and 50° lagging. Therefore, the phase anglebetween voltage V_(An) and current measurement I_(A) ranges from 10°leading to 50° lagging. Likewise, the phase angle between voltage V_(Bn)and current measurement I_(B) ranges from 100 leading to 50° lagging.This is demonstrated by the phasor diagram 62A of FIG. 10A. Because,there is no load connected between phase C and node “n” in 2-phase Wyewiring configuration (FIG.), therefore, I_(C)=0.

The Kirchhoff's current law dictates that the sum of currentmeasurements at node “n” is 0, i.e.,

I _(A) +I _(B)=0.  (9)

According to FIG.,

I _(A) =V _(An) /Z _(A) ,I _(B) =V _(Bn) /Z _(B).  (10)

Substituting equation (10) into equation (9) yields

V _(An) /Z _(A) +V _(Bn) /Z _(B)=0.  (11)

Note that equation (11) can be further simplified using the symmetricload assumption in equation (8).

V _(An) +V _(Bn)=0.  (12)

The voltage measurement V_(AB) is related to V_(An) and V_(Bn) via

V _(AB) =V _(An) −V _(Bn)  (13)

Adding equation (12) to equation (13) yields

V _(AB)=2V _(An)  (14)

Therefore, V_(An)=V_(AB)/2, and V_(Bn)=−V_(AB)/2. The resulting voltagemeasurements V_(AN), V_(BN), and V_(CN), when expressed in phasors, areshown phasor diagram 64 of FIG. 11.

Because I_(C)=0, therefore, if the amplitude of I_(A) is 0, i.e.,|V_(A)|=0, where |•| denotes the amplitude of a phasor quantity, thenthe current sensor 34 intended to measure phase A current must have beenmistakenly associated with phase C current-carrying conductor.

Combining FIGS. 10A and 11 yields FIG. 10B. FIG. 10B is a phasor diagram62B showing relationships between voltage measurements V_(AN), V_(BN),V_(CN), and current measurements I_(A), I_(B). The shaded areas in FIG.10B indicate angular ranges of current measurements with respect tovoltage measurements.

Table 6 summarizes cases from FIG. 10B, and shows the current sensordiagnosis for 2-phase Wye wiring configuration. Note that in Table 6,φ_(A) denotes the phase angle between the voltage measurement V_(AN) andthe current measurement from a current sensor 34 intended to measurephase A current, φ_(B) denotes the phase angle between the voltagemeasurement V_(BN) and the current measurement from a current sensor 34intended to measure phase B current. Because I_(C)=0, the phase anglebetween the voltage measurement V_(CN) and the current measurement froma current sensor intended to measure phase C current, φ_(C), is notavailable.

TABLE 6 Current Sensor Diagnosis for 2-Phase Wye Wiring Configurationφ_(A) φ_(B) φ_(C) 0° ≦ φ_(A) < 20° or I_(A) or −I_(B) 0° ≦ φ_(B) < 20°or — N/A — 320° < φ_(A) < 360° 260° < φ_(B) < 360° 20° < φ_(A) < 140° —20° < φ_(B) < 80° I_(B) or −I_(A) N/A — 140° < φ_(A) < 200° −I_(A) orI_(B) 80° < φ_(B) < 200° — N/A — 200° < φ_(A) < 320° — 200° < φ_(B) <260° −I_(B) or I_(A) N/A —

In a 2-Phase Wye wiring configuration, if a first branch circuit currentsensor 34 is intended to measure phase A current, and a second branchcircuit current sensor 34 is intended to measure phase B current, thenthere are 8 possible scenarios for these particular branch circuitcurrent sensors 34.

-   -   1) The first branch circuit current sensor 34 is wired to phase        A current-carrying conductor with a normal polarity. The second        branch circuit current sensor 34 is wired to phase B        current-carrying conductor with a normal polarity. Consequently,        the current measurement from first branch circuit current sensor        is I_(A), and the current measurement from second branch circuit        current sensor is I_(B).    -   2) The first branch circuit current sensor 34 is wired to phase        A current-carrying conductor with a flipped polarity. The second        branch circuit current sensor 34 is wired to phase B        current-carrying conductor with a normal polarity. Consequently,        the current measurement from first branch circuit current sensor        is −I_(A), and the current measurement from second branch        circuit current sensor is I_(B).    -   3) The first branch circuit current sensor 34 is wired to phase        A current-carrying conductor with a normal polarity. The second        branch circuit current sensor 34 is wired to phase B        current-carrying conductor with a flipped polarity.        Consequently, the current measurement from first branch circuit        current sensor is I_(A), and the current measurement from second        branch circuit current sensor is −I_(B).    -   4) The first branch circuit current sensor 34 is wired to phase        A current-carrying conductor with a flipped polarity. The second        branch circuit current sensor 34 is wired to phase B        current-carrying conductor with a flipped polarity.        Consequently, the current measurement from first branch circuit        current sensor is −I_(A), and the current measurement from        second branch circuit current sensor is −I_(B).    -   5) The first branch circuit current sensor 34 is wired to phase        B current-carrying conductor with a normal polarity. The second        branch circuit current sensor 34 is wired to phase A        current-carrying conductor with a normal polarity. Consequently,        the current measurement from first branch circuit current sensor        is I_(B), and the current measurement from second branch circuit        current sensor is I_(A).    -   6) The first branch circuit current sensor 34 is wired to phase        B current-carrying conductor with a flipped polarity. The second        branch circuit current sensor 34 is wired to phase A        current-carrying conductor with a normal polarity. Consequently,        the current measurement from first branch circuit current sensor        is −I_(B), and the current measurement from second branch        circuit current sensor is I_(A).    -   7) The first branch circuit current sensor 34 is wired to phase        B current-carrying conductor with a normal polarity. The second        branch circuit current sensor 34 is wired to phase A        current-carrying conductor with a flipped polarity.        Consequently, the current measurement from first branch circuit        current sensor is I_(B), and the current measurement from second        branch circuit current sensor is −I_(A).    -   8) The first branch circuit current sensor 34 is wired to phase        B current-carrying conductor with a flipped polarity. The second        branch circuit current sensor 34 is wired to phase A        current-carrying conductor with a flipped polarity.        Consequently, the current measurement from first branch circuit        current sensor is −I_(B), and the current measurement from        second branch circuit current sensor is −I_(A).

According to Table 6, for the first branch current sensor 34, if140°≦φ_(A)<200°, then this first branch current sensor 34 is notcorrectly wired to phase A current-carrying conductor with a normalpolarity. Therefore, cases 2), 4), 5) and 7) from the above list can bedetected as incorrect wiring.

According to Table 6, for the second branch current sensor 34, if200°≦φ_(B)<260°, then this second branch current sensor 34 is notcorrectly wired to phase B current-carrying conductor with a normalpolarity. Therefore, cases 3), 4), 5) and 6) from the above list can bedetected as incorrect wiring.

According to Table 6, for the first branch current sensor 34, if0°≦φ_(A)<20° or 320°≦φ_(A)<360°, and for the second branch currentsensor 34, if 20°≦φ_(B)≦80°, then either case 1) or case 8) from theabove list can result in such detection results.

In this case, to differentiate whether case 1) or case 8) from the abovelist is true, other indicators, such as a label of phase attached to thecurrent sensor, and a label of phase attached to the current-carryingconductor, may aid the final determination.

This description below discloses steps to diagnose current sensors 34for the single-phase 3-wire wiring configuration using the phase anglesbetween voltage measurements V_(AN), V_(BN) and current measurementsI_(A), I_(B), respectively.

According to the single-phase 3-wire wiring configuration (FIG. 7), thevoltage measurements V_(AN), V_(BN), are related to voltages V_(An),V_(Bn) via

V _(AN) =V _(An)  (15)

V _(BN) =V _(Bn)  (16)

Therefore, according to equations (15) and (16), V_(An)=−V_(Bn).

FIG. 12 is a phasor diagram 66 showing the relationships between voltagemeasurements V_(AN), V_(BN), and current measurements I_(A), I_(B). Theshaded areas in FIG. 12 indicate angular ranges of current measurementswith respect to voltage measurements.

Table 7 summarizes cases from FIG. 12, and shows the current sensordiagnosis for single-phase 3-wire wiring configuration. Note that inTable 7, φ_(A) denotes the phase angle between the voltage measurementV_(AN) and the current measurement from a current sensor 34 intended tomeasure phase A current, φ_(B) denotes the phase angle between thevoltage measurement V_(BN) and the current measurement from a currentsensor intended to measure phase B current.

TABLE 7 Current Sensor Diagnosis for Single- Phase 3-Wire WiringConfiguration φ_(A) φ_(B) 0° ≦ φ_(A) < 50° or I_(A) or −I_(B) 0° ≦ φ_(A)< 50° or I_(B) or −I_(A) 350° < φ_(A) < 360° 350° < φ_(A) < 360° 50° <φ_(A) < 170° — 50° < φ_(A) < 170° — 170° < φ_(A) < 230° −I_(A) or I_(B)170° < φ_(A) < 230° −I_(B) or I_(A) 200 < φ_(A) < 350° — 200° < φ_(A) <350° —

According to Table 7, φ_(A) or φ_(B) alone cannot uniquely determinethat the current sensor 34 is correctly associated with the intendedphase current-carrying conductor, and that the current sensor 34 has anormal polarity. For example, for a current sensor intended to measurephase A current, if 0°≦φ_(A)<50° or 350°<φ_(A)<360°, the current sensorcan be either of the following two possible scenarios:

-   -   1) The current sensor 34 is associated with phase A        current-carrying conductor, and has a normal polarity.    -   2) The current sensor 34 is associated with phase B        current-carrying conductor, and at the same time has a flipped        polarity.

In this case, other indicators, such as a label of phase attached to thecurrent sensor, and a label of phase attached to the current-carryingconductor, may aid the final determination.

The single-phase 2-wire wiring configuration is a special case of thesingle-phase 3-wire wiring configuration. FIG. 13 is a phasor diagram 68showing the relationships between voltage measurements V_(AN), V_(BN),and current measurements I_(A), I_(B). The shaded areas in FIG. 13indicate angular ranges of current measurements with respect to voltagemeasurements.

Table 8 summarizes cases from FIG. 13, and shows the current sensordiagnosis for single-phase 2-wire wiring configuration. Note that inTable 8, φ_(A) denotes the phase angle between the voltage measurementV_(AN) and the current measurement from a current sensor 34 intended tomeasure phase A current.

TABLE 8 Current Sensor Diagnosis for Single-Phase 2-Wire WiringConfiguration φ_(A) 0° ≦ φ_(A) < 50° or I_(A) 350° < φ_(A) < 360° 50° <φ_(A) < 170° — 170° < φ_(A) < 230° −I_(A) 200° < φ_(A) < 350° —

Validation of Branch Circuit Current Sensor Diagnosis

In branch circuit monitoring system 2, after current sensor diagnosis asdescribed herein is performed for each branch circuit, the final branchcircuit current sensor diagnosis results can be further validated ifmain current sensors 26 have been installed and configured in the samebranch circuit monitoring system 2. The discussion below discloses stepsto validate branch circuit current sensor diagnosis results using realpower P and reactive power Q.

For each branch circuit current sensor 34, the real power P (in watts)and the apparent power S (in volts·amperes) are available. In addition,the power factor PF is also available. Given a non-zero PF, the reactivepower Q (in vars) is then calculated via

$\begin{matrix}{Q = {\frac{PF}{{PF}} \cdot \sqrt{S^{2} - P^{2}}}} & (17)\end{matrix}$

where |PF| is the absolute value of the power factor.

For the following 4 wiring configurations: 3-Phase 4-Wire Wye, 3-Phase3-Wire Delta, 3-Phase 4-Wire Delta, and 3-Phase Corner-Grounded Delta,once current sensor diagnosis as described herein is completed, eachbranch circuit current sensor 34 is associated with phase Acurrent-carrying conductor 10A, or phase B current-carrying conductor10B, or alternatively phase C current-carrying conductor 10C. A totalphase A real power P_(A,total) is obtained by summing up real powerquantities for all branch circuit current sensors 34 that are associatedwith phase A current-carrying conductor 10A. Similarly, a total phase Breal power P_(B,total) is obtained by summing up real power quantitiesfor all branch circuit current sensors 34 that are associated with phaseB current-carrying conductor 10B, and a total phase C real powerP_(C,total) is obtained by summing up real power quantities for allbranch circuit current sensors 34 that are associated with phase Ccurrent-carrying conductor 10C. Likewise, Q_(A,total), Q_(B,total),Q_(C,total) are obtained for the branch circuit monitoring system 2.

For the branch circuit monitoring system 2 based on the above 4 wiringconfigurations, the total real and reactive power quantities are alsocalculated from the voltage measurements made by main voltage sensors 24and the current measurements made by main current sensor 26. They aredenoted as P′_(A,total), P′_(B,total), P′_(C,total), and Q′_(A,total),Q′_(B,total), Q′_(C,total).

Table 9 below shows a method that may be used to validate branch circuitcurrent sensor diagnosis results for the following 4 wiringconfigurations, 3-Phase 4-Wire Wye, 3-Phase 3-Wire Delta, 3-Phase 4-WireDelta, and 3-Phase Corner-Grounded Delta, according to an exemplaryembodiment of an aspect of the disclosed concept. For example, ifP_(B,total)=P′_(B,total) and Q_(B,total)=Q′_(B,total), then the branchcircuit current sensor diagnosis results are validated OK for allcurrent sensors 34 associated with phase B current-carrying conductors.As another example, if P_(C,total)≠P′_(C,total) orQ_(C,total)≠Q′_(C,total), then the branch circuit current sensordiagnosis results are not validated OK for all current sensors 34associated with phase C current-carrying conductors.

TABLE 9 Validation of Branch Circuit Current Sensor Diagnosis Using3-Phase Real Power and Reactive Power Quantities Phase A P_(A, total) =P′_(A, total) and Branch circuit current sensor diagnosis Q_(A, total) =Q′_(A, total) results are validated OK. P_(A, total) ≠ P′_(A, total) orBranch circuit current sensor diagnosis Q_(A, total) ≠ Q′_(A, total)results are not validated OK. Phase B P_(B, total) = P′_(B, total) andBranch circuit current sensor diagnosis Q_(B, total) = Q′_(B, total)results are validated OK. P_(B, total) ≠ P′_(B, total) or Branch circuitcurrent sensor diagnosis Q_(B, total) ≠ Q′_(B, total) results are notvalidated OK. Phase C P_(C, total) = P′_(C, total) and Branch circuitcurrent sensor diagnosis Q_(C, total) = Q′_(C, total) results arevalidated OK. P_(C, total) ≠ P′_(C, total) or Branch circuit currentsensor diagnosis Q_(C, total) ≠ Q′_(C, total) results are not validatedOK.Following the method outlined above, for the following two wiringconfigurations: 2-Phase Wye and Single-Phase 3-Wire, a total phase Areal power P_(A,total) and a total phase A reactive power Q_(A,total)are obtained by summing up real and reactive power quantities for allbranch circuit current sensors 34 that are associated with phase Acurrent-carrying conductor 10A, and a total phase B real powerP_(B,total) not and a total phase B reactive power Q_(B,total) areobtained by summing up real and reactive power quantities for all branchcircuit current sensors 34 that are associated with phase Bcurrent-carrying conductor 10B.

For same branch circuit monitoring system 2 based on the above 2 wiringconfigurations, the total real and reactive power quantities are alsocalculated from the voltage measurements made by main voltage sensors 24and the current measurements made by main current sensor 26. They aredenoted as P′_(A,total), P′_(B,total), and Q′_(A,total), Q′_(B,total).

Table 10 below shows a method that may be used to validate branchcircuit current sensor diagnosis results for the following 2 wiringconfigurations, 2-Phase Wye and Single-Phase 3-Wire, according toanother exemplary embodiment of an aspect of the disclosed concept.

TABLE 10 Validation of Branch Circuit Current Sensor Diagnosis Using2-Phase Real Power and Reactive Power Quantities Phase A P_(A, total) =P′_(A, total) and Branch circuit current sensor diagnosis Q_(A, total) =Q′_(A, total) results are validated OK. P_(A, total) ≠ P′_(A, total) orBranch circuit current sensor diagnosis Q_(A, total) ≠ Q′_(A, total)results are not validated OK. Phase B P_(B, total) = P′_(B, total) andBranch circuit current sensor diagnosis Q_(B, total) = Q′_(B, total)results are validated OK. P_(B, total) ≠ P′_(B, total) or Branch circuitcurrent sensor diagnosis Q_(B, total) ≠ Q′_(B, total) results are notvalidated OK.

For the Single-Phase 2-Wire wiring configuration, a total phase A realpower P_(A,total) and a total phase A reactive power Q_(A,total) areobtained by summing up real and reactive power quantities for all branchcircuit current sensors 34 that are associated with phase Acurrent-carrying conductor 10A. The total real and reactive powerquantities, denoted as P′_(A,total) and Q′_(A,total), are alsocalculated from the voltage measurements made by main voltage sensors 24and the current measurements made by main current sensor 26.

Table 11 shows the method that may be used to validate branch circuitcurrent sensor diagnosis results for the Single-Phase 2-Wire wiringconfigurations according to a further aspect of the disclosed concept.

TABLE 11 Validation of Branch Circuit Current Sensor Diagnosis UsingSingle-Phase Real Power and Reactive Power Quantities Phase AP_(A, total) = P′_(A, total) and Branch circuit current sensor diagnosisQ_(A, total) = Q′_(A, total) results are validated OK. P_(A, total) ≠P′_(A, total) or Branch circuit current sensor diagnosis Q_(A, total) ≠Q′_(A, total) results are not validated OK.

Wiring Configuration Determination

Provided below is a description of a methodology for determining thenumber of phases in a system, such as branch circuit monitoring system2, and then further determining the wiring configuration of the systemaccording to still a further aspect of the disclosed concept. Thismethodology is, in the exemplary embodiment, accomplished using only theRMS voltage measurements made by voltage sensors 24, 28 and assumesunused voltage terminals of the branch circuit meter modules 14A, 14Bare tied to the neutral voltage node comprising neutral conductor 32.

The methodology of this aspect of the disclosed concept uses Line toLine and Line to Neutral voltage measurements to determine the wiringconfiguration without phase angle information. In particular, thevoltage sensors 24, 28 will provide Line to Neutral voltage measurementsfor each of the conductors 10A, 10B, 10C of main busbar 10 (i.e., eachphase) to branch circuit meter modules 14. From that information, branchcircuit meter modules 14 are able to determine Line to Line voltagemeasurements for each of the conductors 10A, 10B, 10C of main busbar 10(i.e., each phase). In order to distinguish between single phase andpolyphase systems, the methodology first establishes the number ofnon-zero Line to Neutral voltage measurements being made by voltagesensors 24, 28. If there are only two non-zero measurements, it can beestablished that the system is a Single-Phase 2-Wire configuration. Ifthere are three non-zero measurements, the system could be a 2-phaseWye, Single-Phase 3-Wire, or a 3-phase configuration. Furthermore,V_(min) refers to the smallest Line to Line voltage measurement, andV_(max) refers to the largest Line to Line voltage measurement. IfV_(max) is equal to V_(min), the methodology will establish that thesystem is a 3-phase system. If V_(max) is twice the value of V_(min),the methodology will establish that the system is a 2-phase Split. IfV_(max) is larger than V_(min) by a factor of the square root of 3, themethodology will establish that the system is a 2-phase Wye. Oneparticular exemplary embodiment determines the phase mathematically bydetermining the ratio of V_(min):V_(max) and using the followingboundaries (boundaries determined as the midpoint between the twoexpected values):

$\frac{V_{\min}}{V_{\max}} = V_{ratio}$

-   -   if V_(ratio)>0.789 then the wiring configuration is a 3-phase        configuration    -   if V_(ratio)<0.539 then the wiring configuration is a        Single-Phase 3-Wire configuration    -   if 0.789≧V_(ratio)≧0.539 then the wiring configuration is a        2-phase Wye configuration

If, under the methodology, the system is determined to be a 3-phasesystem, the system can be further categorized as a Corner-GroundedDelta, 4-Wire Delta, or a balanced 4-Wire Wye depending on the Line toNeutral voltage measurements. A 3-Phase 3-Wire Delta can be categorizedby the absence of a Line to Neutral voltage measurement. In this aspect,V_(min) refers to the phase with the smallest Line to Neutral voltagemeasurement, and V_(max) refers to the phase with the largest Line toNeutral voltage measurement. Next, the methodology divides V_(min) byV_(max). In the case of a Corner-Grounded Delta, the min value should bezero or close to it. In the case of a 4-Wire Delta, also known as aHigh-Leg Delta or Center-Tapped Delta, the V_(ratio) value is expectedto be close to 1/1.73 or one over the square root of 3. In the case of a4-Wire Wye configuration, V_(ratio) value will be 1 if the system isperfectly balanced, but certainly not much lower than 1. Therefore, anadequate method of distinguishing between the three configurationsidentified above is as follows:

$\frac{V_{\min}}{V_{\max}} = V_{ratio}$$\frac{2}{\sqrt{3} + 1} = {.732}$ $\frac{{.732} + 0}{2} = {.366}$

-   -   if V_(ratio)<0.366 then Voltage Configuration is Corner—Grounded        Delta        -   if 0.366≦V_(ratio)<0.732 then Voltage Configuration is            4—Wire Delta            -   if V_(ratio)>0.732 then Voltage Configuration is 4—Wire                Wye

Diagnosis of Voltage Swap Conditions

A further aspect of the disclosed concept relates to diagnosing voltageswap conditions. For balanced wiring configurations, voltage phases areinterchangeable and indistinguishable from each other. However,configurations that utilize a Neutral Voltage can be miswired byswapping the Neutral with a Phase voltage (referred to as a neutralswap). Also, in configurations with imbalanced voltages, miswiring canoccur between Phases (referred to as a phase swap). Both of thesemiswiring errors can be diagnosed.

Neutral Swap can occur in 3-Phase 4-Wire Wye, 3-Phase 4-Wire Delta, andSingle-Phase 3-Wire configurations. To diagnose Neutral Swaps with anyof the 3-phase configurations, one sample of the Line to Line voltagemeasurements (ie, each phase is sampled) is taken. V_(min) refers to thephase with the smallest Line to Line voltage measurement, and V_(max)refers to the phase with the largest Line to Line voltage measurement.Next, the methodology divides V_(min) by V_(max). The following tables12 and 13 show the possible V_(ratio) values of a 120V_(LN)-based systemfor the correct wiring, and the swapping of Neutral with any phase of a4-Wire Wye or 4-Wire Delta:

TABLE 12 Neutral Swap for 4-Wire Wye Configuration 4-Wire WyeConfiguration Correct N Swap with Phase V_(min) = 208 V V_(min) = 120 VV_(max) = 208 V V_(max) = 208 V V_(ratio) = 1 V_(ratio) = 0.577

TABLE 13 Neutral Swap for 4-Wire Delta Configuration 4-Wire DeltaConfiguration Correct N Swap w/Hi-Leg N Swap w/Lo-Leg V_(min) = 240 VV_(min) = 120 V V_(min) = 120 V V_(max) = 240 V V_(max) = 240 V V_(max)= 208 V V_(ratio) = 1 V_(ratio) = .5 V_(ratio) = 0.577

Therefore, an adequate method of detecting if the measurement point ofneutral conductor 32 has been wired correctly is as follows:

$\frac{V_{\min}}{V_{\max}} = V_{ratio}$$\frac{2}{\sqrt{3} + 1} = {.732}$

-   -   if V_(ratio)>0.732 then the Neutral Has Been Wired Correctly    -   if V_(ratio)≦0.732 then the Neutral Has Been Wired Incorrectly

To diagnose a neutral swap condition with the Single-Phase 3-Wireconfiguration, tone sample of the Line to Neutral voltages of each phaseis taken. V_(A) refers to the first voltage and V_(B) refer to thesecond voltage. If one is lower than the other by ½, then the lower oneis swapped with neutral. The following table 14 shows example values ofa 120V_(LN)-based system for the correct wiring, and the swapping ofNeutral with either phase:

TABLE 14 Neutral Swap for Single-Phase 3-Wire Configuration Single-Phase3-Wire Configuration Correct N Swap w/Phase A N Swap w/Phase B V_(A) =120 V V_(A) = 120 V V_(A) = 240 V V_(B) = 120 V V_(B) = 240 V V_(B) =120 V

A phase swap condition can be detected in the unbalanced phaseconfiguration of 3-Phase 4-Wire Delta with its identification of theHi-leg. According to another aspect of the disclosed concept, one sampleof the Line to Neutral voltages of each phase is taken. V_(A), V_(B),and V_(C) refer to the voltages of each phase. The Hi-leg can then beidentified by the voltage with the highest value. The following table 15shows example values of a 120V_(LN)-based system:

TABLE 15 Phase Swap for Single-Phase 3-Wire Configuration Single-Phase3-Wire Configuration V_(A) is Hi-Leg V_(B) is Hi-Leg V_(C) is Hi-LegV_(A) = 208 V V_(A) = 120 V V_(A) = 120 V V_(B) = 120 V V_(B) = 208 VV_(B) = 120 V V_(C) = 120 V V_(C) = 120 V V_(C) = 208 VA mismatch in the expected Hi-leg from the identified Hi-leg would be amiswire.

Branch Circuit Sensor Grouping

In accordance with a further aspect of the disclosed concept, as part ofthe commissioning process for branch circuit monitoring system 2, branchcircuit sensors 34 are grouped together into virtual meters. These arehighly dependent on the physical layout of branch circuit monitoringsystem 2, and can be diagnosed with information about the physicallayout, and with data from the voltage and current sensors of theassociated pairs.

For a polyphase system, the physical layout of branch circuits (eachbranch circuit being associated with a single pole of a circuit breaker22) is typically in repeating phase order, or in repeating reverse phaseorder. By identifying the position of each branch circuit in thephysical layout of branch circuit monitoring system 2, phase errors canbe found if the branches do not follow one of the prescribed orders.

Below in Table 16 are typical physical layouts for 6 branches of 3-phaseand 2-phase systems. 3-phase or 2-phase systems that don't use one ofthese layouts would generate an error.

TABLE 16 Typical Physical Layouts for 6 Branches of 3-Phase and 2-PhaseSystems Mapping of Physical Layout To Branch Circuit Phases 3-PhaseRepeating Phase Order ABCABC 3-Phase Repeating Reverse Phase OrderCBACBA 2-Phase Repeating Phase Order ABABAB 2-Phase Repeating ReversePhase Order BABABA

One, two, or three branch circuit current sensors 34 can be groupedtogether to create a virtual meter. A virtual meter typically monitorsdifferent phases of the same balanced load 20, such as an HVAC or3-phase motor, and are typically adjacent to each other physically.Thus, a typical virtual meter can define its branch circuits for activeloads according to the following criteria: (i) each branch circuit andthe associated branch circuit current sensor 34 in a virtual metershould link to a different phase with no duplicate phases; (ii) allbranch circuits and the associated branch circuit current sensor 34 in avirtual meter should have the same or similar phase angle; (iii) allbranch circuits and the associated branch circuit current sensor 34 in avirtual meter should have the same or similar current; (iv) all branchcircuits and the associated branch circuit current sensor 34 in avirtual meter should be adjacent in the physical layout By analyzingeach current, phase angle, and position in the physical layout of eachbranch circuit and the associated branch circuit current sensor 34,virtual meters can be identified with a high degree of confidence.

In accordance with the disclosed concept, analysis begins withidentifying the possible virtual meters for each branch circuit and theassociated branch circuit current sensor 34 according to the physicallayout of branch circuit monitoring system 2. For example, Table 17below shows a typical branch circuit in a 3-phase system can be part ofup to 3 possible 3-phase meters or 2 possible 2-phase meters, asillustrated below.

TABLE 17 Possible Virtual Meters for a Typical Branch Circuit Possiblemeters In a 3-phase system For Branch Circuit A 3 possible 3-phase ABCABCA meters ABCABCA ABCA BCA 2 possible 2-phase ABC ABCA meters ABCA BCABranches and the associated branch circuit current sensor 34 locatednear the edge of the physical layout will have fewer possible metersthan those located away from the edge. This method only identifies3-phase meters on 3-phase 4-wire wye and 3-phase 3-wire delta systems,and 2-phase meters on 1-phase 3-wire systems.

Next, for each possible virtual meter, its branch circuit phase anglevariance is calculated using this variance equation:

${\sigma^{2} = \frac{\sum\left( {x - \mu} \right)^{2}}{N}},$

where x is each of the branch circuit phase angles in the possiblevirtual meter, u is the average of the branch circuit phase angles inthe possible virtual meter, and N is the number of branches andassociated branch circuit current sensors 34 in the possible virtualmeter. The branch circuit current variance for each possible virtualmeter is also calculated using the same equation, where x is each of thebranch circuit currents in the possible virtual meter, u is the averageof the branch circuit currents in the possible virtual meter, and N isthe number of branches and associated branch circuit current sensors 34in the possible virtual meter.

Then for each branch circuit and the associated branch circuit currentsensor 34, a candidate virtual meter is determined by comparing all ofthe variances of all the possible virtual meters that include it. If oneof the virtual meters that includes the branch circuit has the lowestbranch circuit phase angle variance and the lowest branch circuitcurrent variance, it is determined to be a candidate virtual meter.Otherwise, there is no candidate virtual meter for that branch.

If there is a possible virtual meter where each of its branch circuitshave determined the possible virtual meter to be their candidate virtualmeter, then that possible virtual meter is identified as a virtual meterwith high confidence. To increase confidence, a filter can be placed onthe variances, such that if the variance between the phase angles orcurrents is too high, no candidate meter is identified.

While specific embodiments of the disclosed concept have been describedin detail, it will be appreciated by those skilled in the art thatvarious modifications and alternatives to those details could bedeveloped in light of the overall teachings of the disclosure.Accordingly, the particular arrangements disclosed are meant to beillustrative only and not limiting as to the scope of the disclosedconcept which is to be given the full breadth of the claims appended andany and all equivalents thereof.

What is claimed is:
 1. A method for determining a wiring configurationof an electric power system, comprising: determining a plurality of Lineto Line voltage measurement values for the electric power system;determining a voltage ratio for the electric power system using aplurality of the Line to Line voltage measurement values; and using thevoltage ratio to determine the wiring configuration of the electricpower system.
 2. The method according to claim 1, wherein thedetermining the voltage ratio comprises: determining a V_(min), whereV_(min) is a minimum of the Line to Line voltage measurement values,determining a V_(max), where V_(max) is a maximum of the Line to Linevoltage measurement values; and determining the voltage ratio as beingequal to V_(min)/V_(max).
 3. The method according to claim 2, whereinthe determining a plurality of Line to Line voltage measurement valuescomprises: obtaining in a branch circuit meter module a first phase Lineto Neutral voltage measurement value for the electric power system, asecond phase Line to Neutral voltage measurement value for the electricpower system, and a third phase Line to Neutral voltage measurementvalue for the electric power system; and determining a first Line toLine voltage measurement value, a second Line to Line voltagemeasurement value, and a third Line to Line voltage measurement value,each using two or more of the first phase Line to Neutral voltagemeasurement value, the second phase Line to Neutral voltage measurementvalue, and the third phase Line to Neutral voltage measurement value;wherein V_(min) is a minimum of the first Line to Line voltagemeasurement value, the second Line to Line voltage measurement value,and the third Line to Line voltage measurement value, and V_(max) is amaximum of the first Line to Line voltage measurement value, the secondLine to Line voltage measurement value, and the third Line to Linevoltage measurement value.
 4. The method according to claim 2, whereinthe using the voltage ratio comprises: (i) determining that the wiringconfiguration is a 3-phase configuration if the voltage ratio is greaterthan a first value; (ii) determining that the wiring configuration is asingle-phase 3-wire configuration if the voltage ratio is less than asecond value; and (iii) determining that the wiring configuration is a2-phase Wye configuration if the voltage ratio is greater than or equalto the second value and less than or equal to the first value.
 5. Themethod according to claim 4, wherein the first value is 0.789 and thesecond value is 0.539.
 6. The method according to claim 4, wherein thedetermining the plurality of Line to Line voltage measurement valuescomprises determining a plurality of Line to Neutral voltage measurementvalues for the electric power system, wherein the method furthercomprises determining a second V_(max), where the second V_(max) is amaximum of the Line to Neutral voltage measurement values, determining asecond V_(min), where the second V_(min) is a minimum of the Line toNeutral voltage measurement values, determining a second voltage ratioequal to the second V_(min)/the second V_(max), and using the secondvoltage ratio to identify the wiring configuration as Corner-GroundedDelta, 4-wire Delta or 4-wire Wye based on the second voltage ratio. 7.The method according to claim 6, wherein: (i) the wiring configurationis identified as Corner-Grounded Delta if the second voltage ratio isless than a third value; (ii) the wiring configuration is identified as4-wire Wye if the second voltage ratio is greater than a fourth value;and (iii) the wiring configuration is identified as 4-wire Delta if thesecond voltage ratio is greater than or equal to the third value andless than or equal to the fourth value.
 8. The method according to claim7, wherein the third value is 0.366 and the fourth value is 0.732.
 9. Abranch circuit meter module for an electric power system, comprising: acontrol system, wherein the control system stores and is structured toexecute a number of routines, the number of routines being structuredto: determine a plurality of Line to Line voltage measurement values forthe electric power system, determine a voltage ratio for the electricpower system using a plurality of the Line to Line voltage measurementvalues; and use the voltage ratio to determine a wiring configuration ofthe electric power system.
 10. The branch circuit meter module accordingto claim 9, wherein the routines are structured to determine the voltageratio by: determining a V_(min), where V_(min) is a minimum of the Lineto Line voltage measurement values; determining a V_(max), where V_(max)is a maximum of the Line to Line voltage measurement values; anddetermining the voltage ratio as being equal to V_(min)/V_(max).
 11. Thebranch circuit meter module according to claim 10, wherein the routinesare structured to determine a plurality of Line to Line voltagemeasurement values by: (i) obtaining in a branch circuit meter module afirst phase Line to Neutral voltage measurement value for the electricpower system, a second phase Line to Neutral voltage measurement valuefor the electric power system, and a third phase Line to Neutral voltagemeasurement value for the electric power system, and (ii) determining afirst Line to Line voltage measurement value, a second Line to Linevoltage measurement value, and a third Line to Line voltage measurementvalue, each using two or more of the first phase Line to Neutral voltagemeasurement value, the second phase Line to Neutral voltage measurementvalue, and the third phase Line to Neutral voltage measurement value;wherein V_(min) is a minimum of the first Line to Line voltagemeasurement value, the second Line to Line voltage measurement value,and the third Line to Line voltage measurement value, and V_(max) is amaximum of the first Line to Line voltage measurement value, the secondLine to Line voltage measurement value, and the third Line to Linevoltage measurement value.
 12. The branch circuit meter module accordingto claim 10, wherein the routines are structured to use the voltageratio to determine the wiring configuration by: (i) determining that thewiring configuration is a 3-phase configuration if the voltage ratio isgreater than a first value; (ii) determining that the wiringconfiguration is a single-phase 3-wire configuration if the voltageratio is less than a second value; and (iii) determining that the wiringconfiguration is a 2-phase Wye configuration if the voltage ratio isgreater than or equal to the second value and less than or equal to thefirst value.
 13. The branch circuit meter module according to claim 12,wherein the first value is 0.789 and the second value is 0.539.
 14. Thebranch circuit meter module according to claim 12, wherein the routinesare structured to determine the plurality of Line to Line voltagemeasurement values by determining a plurality of Line to Neutral voltagemeasurement values for the electric power system, wherein the routinesare further structured to determine a second V_(max), where the secondV_(max) is a maximum of the Line to Neutral voltage measurement values,determine a second V_(min), where the second V_(min) is a minimum of theLine to Neutral voltage measurement values, determine a second voltageratio equal to the second V_(min)/the second V_(max), and use the secondvoltage ratio to identify the wiring configuration as Corner-GroundedDelta, 4-wire Delta or 4-wire Wye based on the second voltage ratio. 15.The branch circuit meter module according to claim 14, wherein: (i) thewiring configuration is identified as Corner-Grounded Delta if thesecond voltage ratio is less than a third value; (ii) the wiringconfiguration is identified as 4-wire Wye if the second voltage ratio isgreater than a fourth value; and (iii) the wiring configuration isidentified as 4-wire Delta if the second voltage ratio is greater thanor equal to the third value and less than or equal to the fourth value.16. The branch circuit meter module according to claim 15, wherein thethird value is 0.366 and the fourth value is 0.732.
 17. A non-transitorycomputer readable medium storing one or more programs, includinginstructions, which when executed by a computer, causes the computer toperform the method of claim
 1. 18. A method for diagnosing a neutralswap condition in an electric power system employing a 3-phase 4-wireWye wiring configuration or a 3-phase 4-wire Delta wiring configuration,comprising: determining a plurality of Line to Line voltage measurementvalues for the electric power system; determining a voltage ratio forthe electric power system using a plurality of the Line to Line voltagemeasurement values; and using the voltage ratio to determine whether theneutral swap condition is present.
 19. The method according to claim 18,wherein the determining the voltage ratio comprises: determining aV_(min), where V_(min) is a minimum of the Line to Line voltagemeasurement values; determining a V_(max), where V_(max) is a maximum ofthe Line to Line voltage measurement values; and determining the voltageratio as being equal to V_(min)/V_(max).
 20. The method according toclaim 19, wherein the using the voltage ratio comprises: (i) determiningthat the neutral swap condition is not present if the voltage ratio isgreater than a predetermined value; and (ii) determining that theneutral swap condition is present if the voltage ratio is less than orequal to the predetermined value.
 21. The method according to claim 20,wherein the predetermined value is 0.732.
 22. A branch circuit metermodule for an electric power system employing a 3-phase 4-wire Wyewiring configuration or a 3-phase 4-wire Delta wiring configuration,comprising: a control system, wherein the control system stores and isstructured to execute a number of routines, the number of routines beingstructured to: determine a plurality of Line to Line voltage measurementvalues for the electric power system; determine a voltage ratio for theelectric power system using a plurality of the Line to Line voltagemeasurement values; and use the voltage ratio to determine whether aneutral swap condition is present in the electric power system.
 23. Thebranch circuit meter module according to claim 22, wherein the routinesare structured to determine the voltage ratio by: determining a V_(min),where V_(min) is a minimum of the Line to Line voltage measurementvalues; determining a V_(max), where V_(max) is a maximum of the Line toLine voltage measurement values; and determining the voltage ratio asbeing equal to V_(min)/V_(max).
 24. The branch circuit meter moduleaccording to claim 23, wherein the routines are structured to use thevoltage ratio by: (i) determining that the neutral swap condition is notpresent if the voltage ratio is greater than a predetermined value; and(ii) determining that the neutral swap condition is present if thevoltage ratio is less than or equal to the predetermined value.
 25. Thebranch circuit meter module according to claim 24, wherein thepredetermined value is 0.732.
 26. A non-transitory computer readablemedium storing one or more programs, including instructions, which whenexecuted by a computer, causes the computer to perform the method ofclaim
 18. 27. A method for diagnosing a neutral swap condition in anelectric power system employing a single-phase 3-wire configuration,comprising: determining a first Line to Neutral voltage measurementvalue for a first phase of the electric power system using a firstvoltage sensor, determining a second Line to Neutral voltage measurementvalue for a second phase of the electric power system using a secondvoltage sensor, and determining that a neutral swap condition existswith respect to the first voltage sensor if the first Line to Neutralvoltage measurement value is lower than the second Line to Neutralvoltage measurement value by at least one half; or determining that aneutral swap condition exists with respect to the second voltage sensorif the second Line to Neutral voltage measurement value is lower thanthe first Line to Neutral voltage measurement value by at least onehalf.
 28. A branch circuit meter module for an electric power systememploying a single-phase 3-wire wiring configuration, comprising: acontrol system, wherein the control system stores and is structured toexecute a number of routines, the number of routines being structuredto: determine a first Line to Neutral voltage measurement value for afirst phase of the electric power system using a first voltage sensor;determine a second Line to Neutral voltage measurement value for asecond phase of the electric power system using a second voltage sensor;determine that a neutral swap condition exists with respect to the firstvoltage sensor if the first Line to Neutral voltage measurement value islower than the second Line to Neutral voltage measurement value by atleast one half; and determine that a neutral swap condition exists withrespect to the second voltage sensor if the second Line to Neutralvoltage measurement value is lower than the first Line to Neutralvoltage measurement value by at least one half.
 29. A non-transitorycomputer readable medium storing one or more programs, includinginstructions, which when executed by a computer, causes the computer toperform the method of claim
 27. 30. A method of diagnosing a phase swapcondition in an electric power system having a first phase, a secondphase and a third phase and employing a 3-phase 4-wire Delta wiringconfiguration having a Hi-leg, wherein the Hi-leg is the first phase,the method comprising: determining a first Line to Neutral voltagemeasurement value for the first phase; determining a second Line toNeutral voltage measurement value for the second phase; determining athird Line to Neutral voltage measurement value for the third phase;determining whether the first Line to Neutral voltage measurement valueis a maximum of the first Line to Neutral voltage measurement value, thesecond Line to Neutral voltage measurement value and the third Line toNeutral voltage measurement value; and detecting that a phase swapcondition is present if the first Line to Neutral voltage measurementvalue is not the maximum.
 31. A branch circuit meter module for anelectric power system having a first phase, a second phase and a thirdphase and employing a 3-phase 4-wire Delta wiring configuration having aHi-leg, wherein the Hi-leg is the first phase, comprising: a controlsystem, wherein the control system stores and is structured to execute anumber of routines, the number of routines being structured to:determine a first Line to Neutral voltage measurement value for thefirst phase; determine a second Line to Neutral voltage measurementvalue for the second phase; determine a third Line to Neutral voltagemeasurement value for the third phase; determine whether the first Lineto Neutral voltage measurement value is a maximum of the first Line toNeutral voltage measurement value, the second Line to Neutral voltagemeasurement value and the third Line to Neutral voltage measurementvalue; and detect that a phase swap condition is present if the firstLine to Neutral voltage measurement value is not the maximum.
 32. Anon-transitory computer readable medium storing one or more programs,including instructions, which when executed by a computer, causes thecomputer to perform the method of claim
 30. 33. A method of identifyingvirtual meters in an electric power system employing a 3-phase 4-wirewye, a 3-phase 3-wire delta, or a 1-phase 3-wire wiring configurationand having a plurality of branch circuits and a plurality of branchcircuit current sensors, wherein each of the branch circuit currentsensors is associated with a respective one of the branch circuits, andwherein the branch circuits and the branch circuit current sensors arearranged in a physical layout wherein the branch circuits and theassociated branch circuit current sensors are positioned in seriesadjacent to one another, the method comprising; determining a phaseassociation for each of the branch circuit current sensors; testing thephysical layout using each phase association to determine whether thebranch circuit current sensors are arranged in repeating phase order orreverse repeating phase order; responsive to determining that the branchcircuit current sensors are arranged in repeating phase order or reverserepeating phase order, for each branch circuit and the associated branchcircuit current sensor: (i) identifying a plurality of possible virtualmeters including the associated branch circuit current sensor; (ii) foreach possible virtual meter, calculating an associated measure of branchcircuit phase angle variance and an associated measure branch circuitcurrent variance; and (iii) determining a candidate virtual meter forthe branch circuit based on the associated measures of branch circuitphase angle variance and the associated measures of branch circuitcurrent variances; determining a number of identified virtual meterseach including two or more of the branch circuit current sensors basedon the candidate virtual meters.
 34. The method according to claim 33,wherein for each branch circuit and the associated branch circuitcurrent sensor the identifying comprises identifying one to threepossible 3-phase virtual meters including the associated branch circuitcurrent sensor and one to two possible 2-phase virtual meters includingthe associated branch circuit current sensor, and wherein thecalculating includes calculating, for each possible 3-phase virtualmeter and each possible 2-phase virtual meter, an associated measure ofbranch circuit phase angle variance and an associated measure of branchcircuit current variance.
 35. A branch circuit meter module for anelectric power system employing a 3-phase 4-wire wye, a 3-phase 3-wiredelta, or a 1-phase 3-wire wiring configuration and having a pluralityof branch circuits and a plurality of branch circuit current sensors,wherein each of the branch circuit current sensors is associated with arespective one of the branch circuits, and wherein the branch circuitsand the branch circuit current sensors are arranged in a physical layoutwherein the branch circuits and the associated branch circuit currentsensors are positioned in series adjacent to one another, comprising: acontrol system, wherein the control system stores and is structured toexecute a number of routines, the number of routines being structuredto: determine a phase association for each of the branch circuit currentsensors; testing the physical layout using each phase association todetermine whether the branch circuit current sensors are arranged inrepeating phase order or reverse repeating phase order; responsive todetermining that the branch circuit current sensors are arranged inrepeating phase order or reverse repeating phase order, for each branchcircuit and the associated branch circuit current sensor: (i) identify aplurality of possible virtual meters including the associated branchcircuit current sensor, (ii) for each possible virtual meter, calculatean associated measure of branch circuit phase angle variance and anassociated measure branch circuit current variance; and (iii) determinea candidate virtual meter for the branch circuit based on the associatedmeasures of branch circuit phase angle variance and the associatedmeasures of branch circuit current variances; determine a number ofidentified virtual meters each including two or more of the branchcircuit current sensors based on the candidate virtual meters.
 36. Thebranch circuit meter module according to claim 35, wherein for eachbranch circuit and the associated branch circuit current sensor theroutines are structured to identify one to three possible 3-phasevirtual meters including the associated branch circuit current sensorand one to two possible 2-phase virtual meters including the associatedbranch circuit current sensor, and wherein the routines are structuredto calculate, for each possible 3-phase virtual meter and each possible2-phase virtual meter, an associated measure of branch circuit phaseangle variance and an associated measure of branch circuit currentvariance.
 37. A non-transitory computer readable medium storing one ormore programs, including instructions, which when executed by acomputer, causes the computer to perform the method of claim 33.